Last week I spent some time with an entrepreneur I know. When I last saw him he was training for an Ironman, that inexplicable race in which you swim a couple of miles then cycle as far as London to Brighton and back and then finish up with a marathon.

This time he announced he was going further. Marathons simply weren’t demanding enough for him. The previous week he had run a marathon and a half, and his Fitbit had recorded his personal best number of steps in a day: 50,000.

While he has been thrashing his body in this way, he has also been putting superhuman effort into building a business. The two activities, he insists, are complementary. Stamina translates from one to the other.

The previous weekend I had read, in an interview in the Times, that Harriet Green, chief executive of Thomas Cook, likes to start her day in the gym at 5.30am hefting 16kg kettlebells and has energy even her personal trainer cannot match.

She also believes that there is a link between the punishment she exerts on her body and the bottom line of her business. She builds strength in the gym, which is just what is needed to rescue a travel company in deep trouble and turn it into something that is now the object of a Harvard Business School case study.

Executives have long boasted about the rigour of their gym routines but this extreme exercise is getting out of hand. As business gets more competitive we all talk of the need for companies to be “lean” and “fit”, “agile”, “flexible” and to “sweat” the small stuff. But do we really mean the bodies of their leaders must fit the same description?

In a limited way, some exercise helps us perform at work. When I get up off my bottom and climb the stairs or ride somewhere on my bike I feel less sluggish as a result. But to achieve this pleasant state of perkiness there is no need for 16kg weights or for running 39 miles. According to the National Health Service website all you need to do is go for a shortish, briskish walk five times a week.

And even this amount of activity isn’t a prerequisite of dazzling business success. The two leaders I most admire are both on the heavy side and I have never known either to take any exercise at all.

Exceptionally large brain

Each has a large body that houses an exceptionally large brain. They both seem to have plenty of stamina for running a big, complex business, both take good decisions and are much looked up to by the many thousands of people that work for them.

It is true that these are exceptions: there are far more fitness fanatics than fatties in corporate boardrooms. Yet the reason is not that extreme exercise causes extreme success, more that both are the result of the same personality defect.

Corporate success requires a pathological amount of motivation and discipline, as does building abs to a size God never intended when he fashioned Adam and Eve from clay.

The only pity is that such discipline is wasted on something so inward and pointless. Almost anything would be better – learning to play the violin, reading a book or even going shopping – as at least you are giving the economy a boost. Sport does not broaden an executive’s worldview. Virtually everything else does.

Not only is excessive exercise not necessary for success, it is a bad idea for at least four reasons. First, it is terrible for families, as if you work long hours then exercise long hours you really never see them at all.

Discriminatory

Second, it is discriminatory. People who sweat together form a bond that excludes other people. It is no coincidence that Ms Green has filled her top team at Thomas Cook with a marathon runner, a triathlete and a former gymnast.

Third, it makes people feel not just superior but invincible in a way that can be dangerous. In business it is quite good to feel vulnerable and well aware of your weaknesses. Only the paranoid survive, and all that.

But my main complaint is that people who go on about their Fitbits are excruciatingly dull. In the Financial Times about a week ago David Hockney described walking through the park one day, cigarette in hand, on the way to visit his mate Lucian Freud, enjoying the sight of magpies and rabbits as he went. Three girls jogged past whom, he said, didn't see the magpies or the rabbits as they were thinking only of their bodies.

To the painter, who at 77 knows something about stamina, a gentle stroll is far better than running, not only because you look at things but also because it is kinder on your shins. This final argument – that excessive exercise is bad for your bones – is one I don’t want to stoop to using, however. If executives choose to mess with their skeletons in this way, let them. It is none of my business. – Copyright The Financial Times Ltd 2014